Architecture of a low bandwidth predistortion system for non-linear RF components

ABSTRACT

Systems and methods for compensating for non-linearity of a non-linear subsystem using predistortion are disclosed. In one embodiment, a system includes a non-linear subsystem and a predistorter configured to effect predistortion of an input signal of the non-linear subsystem such that the predistortion compensates for a non-linear characteristic of the non-linear subsystem. In addition, the system includes a narrowband filter that filters a feedback signal that is representative of an output signal of the non-linear subsystem to provide a filtered feedback signal, and an adaptor that adaptively configures the predistorter based on the filtered feedback signal and a reference signal that is representative of an input signal of the non-linear subsystem. By utilizing the filtered feedback signal, rather than the feedback signal, a complexity, and therefore, cost of the adaptor is substantially reduced.

RELATED APPLICATIONS

This application is related to U.S. patent application Ser. No.13/333,391, entitled ARCHITECTURE OF NONLINEAR RF FILTER-BASEDTRANSMITTER, which was filed Dec. 21, 2011; and U.S. patent applicationSer. No. 13/333 407, entitled ADAPTIVE PREDISTORTION FOR A NON-LINEARSUBSYSTEM BASED ON A MODEL AS A CONCATENATION OF A NON-LINEAR MODELFOLLOWED BY A LINEAR MODEL, which was filed Dec. 21, 2011; both of whichare commonly owned and assigned and are hereby incorporated herein byreference in their entireties.

FIELD OF THE DISCLOSURE

The present disclosure relates to linearization of a non-linearsubsystem using predistortion and, in many embodiments, relates tolinearization of a non-linear filter at an output of a radio frequencytransmitter using predistortion.

BACKGROUND

Every node in a communication network that desires to send data musthave a transmitter. For instance, in a cellular communication network,transmitters are found in base stations as well as user equipmentdevices, or terminals. FIG. 1 illustrates one embodiment of aconventional transmitter 10. The transmitter 10 may be a transmitter ofa wireless base station or a transmitter of a user equipment device. Asshown, the transmitter 10 includes a digital-to-analog converter (DAC)12 followed by a modulator and upconverter 14. The output of themodulator and upconverter 14 is amplified by a power amplifier (PA) 16and then filtered by a filter 18. FIG. 2 illustrates another embodimentof the conventional transmitter 10, which is similar to that illustratedin FIG. 1. However, in this embodiment, the transmitter 10 includes adigital predistorter (DPD) 20 that operates to predistort the inputsignal to compensate for a non-linearity of the PA 16. An adaptor 22adaptively configures the digital predistorter 20 based on the inputsignal and a feedback signal provided from the output of the PA 16 via ademodulator and downconverter 24 and an analog-to-digital converter(ADC) 26.

Ideally, the filter 18 is a linear filter. However, all analog filters,including the filter 18, have a non-linear characteristic region. Thenon-linear characteristic of the filter 18 results in severaldisadvantages when the transmitter 10 is implemented in a base stationof a cellular communication network for 4-th Generation (4G) cellularcommunication networks such as, for example, Long Term Evolution (LTE)cellular communication networks. More specifically, next generationcellular communication networks will have macro base stations thatoperate at a high output power (e.g., ˜80 watt (W) average power and˜400 W peak power) and low power base stations that operate at a loweroutput power (e.g., 0.1 to 10 or 20 W). With respect to the high powerbase stations, the only type of filter that can handle the high outputpower is a cavity filter. However, due to the non-linearity issue of thecavity filters the first round production yield of the cavity filtermanufacturing is just around 60%. As such, manufacturing of cavityfilters is very expensive. Therefore, there is a need for improving thenon-linearity issue of the cavity filters to reduce the manufacturingcost.

As for the low power base stations, cavity filters can easily handle thedesired output power while providing the desired linearity. However,cavity filters are very large and heavy as compared to other types offilters (e.g., ceramic filters or monoblock filters). Therefore, the useof cavity filters is not desired for the low power base stations.However, the ceramic filters and monoblock filters do not provide thedesired linearity when operating in higher power, for example, higherthan 5 W. Thus, there is a need for improving the non-linearities of theceramic filters and monoblock filters so that the low power basestations operating in power range from 5 W to 20 W can use such filtersinstead of using the bulky cavity filter.

The conventional transmitter 10 also results in issues when implementedin user equipment devices for 4G cellular communication networks suchas, for example, LTE cellular communication networks. Specifically, whenthe conventional transmitter 10 is implemented in a user equipmentdevice, the filter 18 is a miniature filter such as a Surface AcousticWave (SAW) filter, a Film Bulk Acoustic Resonator (FBAR) filter, or aBulk Acoustic Wave (BAW) filter. The peak power of the PA 16 in 4Gcellular communication networks could push up the filter 18 to work inits non-linear region. As a result, the non-linearity of the filterwould be an issue to the system. So, there is also a need for improvingthe nonlinearities of the miniature filters so that such miniaturefilters can be used in the user equipment devices for 4G wirelessnetworks without communication quality degradation.

All of the issues discussed above stem from non-linearity that thefilter 18 will show when it works above a certain power level and in itsnon-linear characteristic region. Therefore, there is a need for systemsand methods for decreasing or eliminating the non-linearity of anon-linear filter.

SUMMARY

Systems and methods for compensating for non-linearity of a non-linearsubsystem using predistortion are disclosed. In one embodiment, a systemincludes a non-linear subsystem and a predistorter configured to effectpredistortion of an input signal of the non-linear subsystem such thatthe predistortion compensates for a non-linear characteristic of thenon-linear subsystem. In addition, the system includes a narrowbandfilter that filters a feedback signal that is representative of anoutput signal of the non-linear subsystem to provide a filtered feedbacksignal, and an adaptor that adaptively configures the predistorter basedon the filtered feedback signal and a reference signal that isrepresentative of an input signal of the non-linear subsystem. Byutilizing the filtered feedback signal, rather than the feedback signal,a complexity, and therefore, cost of the adaptor is substantiallyreduced.

In one embodiment, the system also includes a second narrowband filterthat filters the reference signal representative of an input signal tothe non-linear subsystem to provide a filtered reference signal, and theadaptor adaptively configures the predistorter based on the filteredfeedback signal and the filtered reference signal.

In one embodiment, the system is a transmitter that includes a poweramplifier configured to amplify a radio frequency input signal toprovide an amplified radio frequency signal, and the non-linear systemis a non-linear filter configured to filter the amplified radiofrequency signal to provide an output signal.

Those skilled in the art will appreciate the scope of the presentdisclosure and realize additional aspects thereof after reading thefollowing detailed description of the preferred embodiments inassociation with the accompanying drawing figures.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

The accompanying drawing figures incorporated in and forming a part ofthis specification illustrate several aspects of the disclosure, andtogether with the description serve to explain the principles of thedisclosure.

FIG. 1 illustrates one embodiment of a conventional transmitter;

FIG. 2 illustrates another embodiment of the conventional transmitter;

FIG. 3 graphically illustrates an input-output characteristic of atypical passive type filter showing that the passive type filter has anon-linear characteristic region at higher power levels and istherefore, in fact, a non-linear filter;

FIG. 4 graphically illustrates relationships between fundamental andlower orders of Intermodulation Distortion (IMD) and harmonics for atypical non-linear filter;

FIGS. 5A and 5B illustrate a transmitter that provides predistortion tocompensate for a non-linear characteristic of a non-linear filteraccording to a first embodiment of the present disclosure;

FIG. 6 illustrates a transmitter that provides predistortion tocompensate for a non-linear characteristic of a non-linear filteraccording to a second embodiment of the present disclosure;

FIG. 7 illustrates a transmitter that provides predistortion tocompensate for a non-linear characteristic of a non-linear filteraccording to a third embodiment of the present disclosure;

FIG. 8 illustrates a transmitter that provides predistortion tocompensate for a non-linear characteristic of a non-linear filteraccording to a fourth embodiment of the present disclosure;

FIG. 9 illustrates a transmitter that provides predistortion tocompensate for a non-linear characteristic of a non-linear filteraccording to a fifth embodiment of the present disclosure;

FIG. 10 illustrates a transmitter that provides predistortion tocompensate for a non-linear characteristic of a non-linear filteraccording to a sixth embodiment of the present disclosure;

FIG. 11 illustrates a transmitter that provides predistortion tocompensate for a non-linear characteristic of a non-linear filteraccording to a seventh embodiment of the present disclosure;

FIG. 12 illustrates a transmitter that provides predistortion tocompensate for a non-linear characteristic of a non-linear filteraccording to an eighth embodiment of the present disclosure;

FIG. 13 illustrates a transmitter that provides predistortion tocompensate for a non-linear characteristic of a non-linear filteraccording to a ninth embodiment of the present disclosure;

FIG. 14 graphically compares operating regions of a typical non-linearfilter with and without predistortion according to one embodiment of thepresent disclosure;

FIG. 15 illustrates a model of non-linear filter that separately modelsan undesired non-linear filter characteristic and a desired linearfilter characteristic of the non-linear filter according to oneembodiment of the present disclosure;

FIG. 16 illustrates one embodiment of an adaptor for adaptivelyconfiguring a predistorter that predistorts for a non-linear filter of atransmitter based on the model of the non-linear filter of FIG. 15according to one embodiment of the present disclosure;

FIGS. 17 through 19 are more detailed illustrations of the non-linearfilter model of FIG. 15 according to one embodiment of the presentdisclosure;

FIG. 20 illustrates an integrated model for the non-linear filter thatis equivalent to the model of the non-linear filter of FIG. 15 but thatcan be solved using conventional adaptive filtering schemes according toone embodiment of the present disclosure;

FIG. 21 illustrates one embodiment of an adaptor for adaptivelyconfiguring a predistorter that predistorts for a non-linear filter of atransmitter based on the model of the non-linear filter of FIG. 15 wherethe non-linear filter model is trained using the integrated model ofFIG. 20 according to one embodiment of the present disclosure;

FIG. 22 illustrates use of an integrated model for a non-linearsubsystem according to one embodiment of the present disclosure;

FIG. 23 illustrates one embodiment of a transmitter including apredistorter that compensates for a non-linearity of a non-linear filterin the transmitter and an adaptor that adaptively configures thepredistorter based on a reduced bandwidth feedback signal according toone embodiment of the present disclosure;

FIGS. 24A through 24D are frequency domain representations of signals atvarious reference points in the transmitter of FIG. 23 according to oneembodiment of the present disclosure; and

FIG. 25 illustrates a system including a non-linear subsystem, apredistorter that compensates for a non-linear characteristic of thenon-linear subsystem, and an adaptor that adaptively configures thepredistorter based on a reduced bandwidth feedback signal according toone embodiment of the present disclosure.

DETAILED DESCRIPTION

The embodiments set forth below represent the necessary information toenable those skilled in the art to practice the embodiments andillustrate the best mode of practicing the embodiments. Upon reading thefollowing description in light of the accompanying drawing figures,those skilled in the art will understand the concepts of the disclosureand will recognize applications of these concepts not particularlyaddressed herein. It should be understood that these concepts andapplications fall within the scope of the disclosure and theaccompanying claims.

Systems and methods for compensating for non-linearity of a non-linearsubsystem using predistortion are disclosed. Before describing thesesystems and methods, it is beneficial to first discuss the non-linearcharacteristic of a passive type filter. Specifically, FIG. 3illustrates an input-output characteristic of a typical passive typefilter. As illustrated, an output power (P_(OUT)) of the filter can bedescribed as P_(OUT)=P_(LINEAR)−P_(NON-LINEAR). A point “A” is a definedpoint below which a non-linear characteristic (i.e., a non-linear part,P_(NON-LINEAR)=P_(LINEAR)−P_(OUT)) of the filter is negligible and canbe ignored such that, when operating below that point, the filter can betreated as a linear filter. However, in the region above point A, thenon-linear characteristic (P_(NON-LINEAR)) gradually increases and mustbe taken into consideration. In other words, above point A, the filtermust be treated as a non-linear filter.

The non-linear characteristic of the filter can be described by thefollowing power series expansion equation:V _(OUT) =a ₀ +a ₁ V _(IN) +a ₂ V _(IN) ² +a ₃ V _(IN)+  (1)The non-linear terms in Equation (1) describe all types ofIntermodulation Distortion (IMD) signals and harmonics that will begenerated by the filter. The relationship between fundamental signalsand lower orders of the IMD signals and harmonics is illustrated in FIG.4. For radio frequency front-end filters in radio frequency transmitterapplications, the most significant distortion signals generated due tothe non-linear characteristic of the filter are 3^(rd), 5^(th) and7^(th) orders IMD signals. These orders IMD signals not only occur outof the passband, but also distribute throughout the entire passband. Assuch, for linearization, it is important to cancel, or at leastsubstantially cancel these orders IMD signals from the filter output.Among other things, the systems and methods described herein utilizepredistortion techniques to provide such linearization.

FIGS. 5A through 13 illustrate embodiments of a transmitter 28 thatcompensates for a non-linear characteristic of a non-linear filter 30 atan output of the transmitter 28 according to the present disclosure.Specifically, FIG. 5A illustrates an embodiment of the transmitter 28that includes a digital-to-analog converter (DAC) 32, a modulator andupconverter 34, a power amplifier (PA) 36, an analog predistorter 38,and the non-linear filter 30. The DAC 32 receives a digital input signaland converts the digital input signal into an analog input signal. Themodulator and upconverter 34 modulates the analog input signal accordingto a desired modulation scheme and upconverts the analog input signal toa desired radio frequency. The radio frequency (RF) signal output by themodulator and upconverter 34 is amplified to a desired output powerlevel by the PA 36 to provide an amplified RF signal. In thisembodiment, the analog predistorter 38 applies a predetermined, fixedpredistortion to the amplified RF signal to provide a predistorted RFsignal. The predistortion applied by the analog predistorter 38compensates for the non-linear characteristic of the non-linear filter30. The predistortion may be predetermined using any suitable technique.The predistorted signal is then filtered by the non-linear filter 30 toprovide an output signal of the transmitter 28. As a result of thepredistortion, the output signal is as if the non-linear filter 30 werea linear, or substantially linear, filter.

FIG. 5B is substantially the same as that of FIG. 5A but where the DAC32 moved after the modulator and upconverter 34. FIG. 5B illustratesthat the concepts discussed herein are independent of the DAC placement.Further, while not discussed further below, it should be understood thatwhile the placement of the DACs in the embodiments below is shown asbeing before modulation and upconversion, the present disclosure is notlimited thereto.

FIG. 6 illustrates an embodiment of the transmitter 28 that is similarto that of FIG. 5A. However, in this embodiment, the transmitter 28 alsoincludes a digital predistorter (DPD) 40 that compensates fornon-linearity of the PA 36. The digital predistorter 40 is adaptivelyconfigured by an adaptor 42 based on the digital input signal and afeedback signal. Specifically, a demodulator and downconverter 44receives a RF feedback signal that is representative of the amplified RFsignal output by the PA 38. The output of the demodulator anddownconverter 44 is digitized by an analog-to-digital converter (ADC) 46to provide the feedback signal to the adaptor 42. The adaptor 42configures the digital predistorter 40 based on a comparison of thedigital input signal and the feedback signal using any suitable adaptivepredistortion scheme. For instance, in one embodiment, the digitalpredistorter 40 provides polynomial predistortion where thepredistortion to compensate for the non-linearity of the PA 38 isdefined by a polynomial having a number of configurable coefficients.The adaptor 42 adaptively configures the coefficients for the polynomialto provide the appropriate predistortion using known techniques.

FIGS. 7 through 9 illustrate embodiments of the transmitter 28 wherepredistortion to compensate for the non-linear characteristic of thenon-linear filter 30 is performed in the digital, rather than analog,domain. Specifically, FIG. 7 illustrates an embodiment of thetransmitter 28 that includes a digital predistorter (DPD) 48 thatcompensates for the non-linear characteristic of the non-linear filter30, a digital predistorter (DPD) 50 that compensates for thenon-linearity of the PA 36, the DAC 32, the modulator and upconverter34, the PA 36, and the non-linear filter 30 connected as shown. Thedigital predistorter 48 applies a predistortion to a digital inputsignal to provide a first predistorted signal that has been predistortedto compensate for the non-linear characteristic of the non-linear filter30. The digital predistorter 50 then applies a predistortion to thefirst predistorted signal to provide a second predistorted signal thathas also been predistorted to compensate for the non-linearity of the PA36. In this embodiment, both the predistortion applied by the digitalpredistorter 48 and the predistortion applied by the digitalpredistorter 50 are predetermined and fixed. The DAC 32 then convertsthe second predistorted signal to an analog signal. The analog signalfrom the DAC 32 is then modulated and amplified by the modulator andupconverter 34. The PA 36 then amplifies the RF signal output from themodulator and upconverter 34 to provide an amplified RF signal that isthen filtered by the non-linear filter 30. Due to the predistortionapplied by the digital predistorter 48, the output signal from thenon-linear filter 30 is as if the non-linear filter 30 was a linear, orsubstantially linear, filter. Note that the digital predistorter 50, theDAC 32, the modulator and upconverter 34, and the PA 36 operate togetheras a linear part 52, or linear sub-system.

FIG. 8 illustrates an embodiment of the transmitter 28 where the digitalpredistorters 48 and 50 (FIG. 7) have been combined into a singledigital predistorter (DPD) 54. The digital predistorter 54 applies apredetermined and fixed predistortion that compensates for both thenon-linearity of the PA 36 and the non-linear characteristic of thenon-linear filter 30.

FIG. 9 illustrates an embodiment of the transmitter 28 that is similarto that of FIG. 7. However, in this embodiment, the transmitter 28 alsoincludes a digital predistorter (DPD) 56 that compensates fornon-linearity of the PA 36. The digital predistorter 56 is adaptivelyconfigured by an adaptor 58 based on the first predistorted signal fromthe digital predistorter 48 and a feedback signal. Specifically, ademodulator and downconverter 60 receives a RF feedback signal that isrepresentative of the amplified radio frequency output signal output bythe PA 36. The output of the demodulator and downconverter 60 isdigitized by an analog-to-digital converter (ADC) 62 to provide thefeedback signal to the adaptor 58. The adaptor 58 configures the digitalpredistorter 56 based on a comparison of the first predistorted signalfrom the digital predistorter 48 and the feedback signal using anysuitable adaptive predistortion scheme. For instance, in one embodiment,the digital predistorter 56 provides polynomial predistortion where thepredistortion to compensate for the non-linearity of the PA 36 isdefined by a polynomial having a number of configurable coefficients.The adaptor 58 adaptively configures the coefficients for the polynomialto provide the appropriate predistortion using known techniques.

FIGS. 10 through 13 illustrate embodiments of the transmitter 28providing adaptive predistortion to compensate for the non-linearcharacteristic of the non-linear filter 30. Specifically, FIG. 10illustrates an embodiment of the transmitter 28 that is similar to thatof FIG. 7. However, in this embodiment, the transmitter 28 includes adigital predistorter (DPD) 64 that compensates for non-linearity of thenon-linear filter 30, where the digital predistorter 64 is adaptivelyconfigured by an adaptor 66 based on the digital input signal and afeedback signal. Specifically, a demodulator and downconverter 68receives a RF feedback signal that is representative of the outputsignal output by the non-linear filter 30. The output of the demodulatorand downconverter 68 is digitized by an analog-to-digital converter(ADC) 70 to provide the feedback signal to the adaptor 66. The adaptor66 configures the digital predistorter 64 based on the digital inputsignal and the feedback signal using any suitable adaptive predistortionscheme. For instance, in one embodiment, the digital predistorter 64provides polynomial predistortion where the predistortion to compensatefor the non-linear characteristic of the non-linear filter 30 is definedby a polynomial having a number of configurable coefficients. Theadaptor 66 adaptively configures the coefficients for the polynomial toprovide the appropriate predistortion.

FIG. 11 illustrates an embodiment of the transmitter 28 that is similarto that of FIG. 10. However, in this embodiment, the transmitter 28 alsoincludes adaptive predistortion for the PA 36 in the manner describedabove with respect to FIG. 9.

FIGS. 12 and 13 are similar to FIGS. 10 and 11, respectively. However,in the embodiments of FIGS. 12 and 13, the digital predistorter 64 isconfigured by an adaptor 72 based on a reference signal that correspondsto the input signal of the non-linear filter 30 and a feedback signalthat corresponds to the output signal of the non-linear filter 30.

FIG. 14 graphically illustrates operating regions for the non-linearfilter 30 with and without predistortion according to one exemplaryembodiment. As illustrated, point “A” is a defined boundary point belowwhich the non-linear filter 30 is treated as linear. Withoutpredistortion, in order to ensure linearity, the non-linear filter 30must operate within operating region 74 where P_(IN) is average inputpower and P_(IN-A) is peak input power. Thus, in order to ensurelinearity, the peak input power must be less than or equal to the inputpower level defined by point A. In contrast, by using predistortion tocompensate for the non-linear characteristic of the non-linear filter30, the non-linear filter 30 is enabled to operate within operatingregion 76. In other words, as a result of the predistortion, linearityis maintained even though the non-linear filter 30 is operating in itsnon-linear region. As a result, with predistortion, the non-linearfilter 30 is linearized below a point “B”. In this case, the averageinput power is P_(IN-PD) and the peak input power is P_(IN-B), whereP_(IN-PD) is much greater than P_(IN) and P_(IN-B) is substantiallygreater than P_(IN-A).

The benefits of predistorting compensate for the non-linearcharacteristic of the non-linear filter 30 including, for example,taking greater advantage of the power handling capabilities of thenon-linear filter 30. In other words, using predistortion, linearity canbe maintained over a much larger power range for a particular type offilter. As a result, with predistortion, a ceramic or monoblock filtercan be used for low power base stations that operate in higher powerlevel, for example higher than 5 W, thereby avoiding the need for bulkycavity type filters. As another example, by using predistortion in thesystem to compensate for the nonlinearities of the cavity filters, themanufacturing yield for cavity type filters can jump right away fromcurrent 60% to nearly 100% in the first round of cavity filtermanufacturing, because the non-linearity specification is no longer arequirement for the cavity filter production. In other words, the costlyfilter non-linearity-fixing process for the cavity filters failed in thefirst round can be eliminated; as a result, the average cavity filtermanufacturing cost can get a great reduction. As yet another example,with predistortion, conventional miniature filters may be used for userequipment devices in next generation and future generation cellularcommunication networks, which require or will likely require greaterdynamic power range.

Now that a number of architectures for the transmitter 28 have beendescribed, the discussion will now turn to embodiments of the adaptor 72of FIGS. 12 and 13. Note, however, that the concepts discussed above forthe adaptor 72 can easily be extended to the adaptor 66 of FIGS. 10 and11. In general, the adaptor 72 operates to adaptively configure thedigital predistorter 64 to compensate for, or counteract, the non-linearcharacteristic of the non-linear filter 30. However, the digitalpredistorter 64 has both the undesired and unknown non-linearcharacteristic and a desired and known linear characteristic. Theadaptor 72 is to operate such that the digital predistorter 64compensates for only the non-linear characteristic of the non-linearfilter 30. However, an issue arises in that the non-linear filter 30 isa physical device that does not include a reference point for only thenon-linear characteristic. Specifically, the output of the non-linearfilter 30 cannot be used as a reference point for the non-linearcharacteristic of the non-linear filter 30 because the output of thenon-linear filter 30 represents both the non-linear characteristic andthe linear characteristic of the non-linear filter 30.

FIG. 15 illustrates a model 78 for the non-linear filter 30 that can beutilized to provide a reference point for adaptive configuration of thedigital predistorter 64 for predistortion of the non-linearcharacteristic of the non-linear filter 30 according to one embodimentof the present disclosure. While the following discussion focuses on theuse of the model 78 for adaptation of the digital predistorter 64 tocompensate for the non-linear characteristic of the non-linear filter30, the model 78 is not limited thereto. The model 78 may be used tomodel any non-linear system, and particularly any non-linear physicaldevice, having an undesired non-linear characteristic and a desiredlinear characteristic. Further, the model 78 may then be used foradaptive predistortion to compensate for the non-linear characteristicof the non-linear system.

As illustrated, the model 78 for the non-linear filter 30 is aconcatenation of a non-linear filter model 80, which also referred toherein as model A, and a linear filter model 82, which is also referredto herein as model B. The non-linear filter model 80 is a model of theundesired and unknown non-linear characteristic of the non-linear filter30. The non-linear characteristic of the non-linear filter 30 may varyover time and/or may vary from one device to another. The linear filtermodel 82 is a model of the desired and known linear characteristic ofthe non-linear filter 30. In other words, the linear filter model 82 isa model of the known linear characteristic of the non-linear filter 30when operating in its linear region. The linear characteristic does notvary over time and is known either by design or by measurement on a perdevice basis to take device variations into consideration. Together, theconcatenation of the non-linear filter model 80 and the linear filtermodel 82 represent the actual response of the non-linear filter 30particularly when operating in its non-linear region.

As discussed below, the non-linear filter model 80 may model thenon-linear characteristic of the non-linear filter 30 using a variabletapped delay line followed by a weighting and summation with a number ofcoefficients (determined via adaptation). As a special case, when thereis only one tap, the non-linear filter model 80 is a memory-lessnon-linear function. In this case, the output of the non-linear filtermodel 80 only depends on the current input of the non-linear filtermodel 80 and not any of its previous inputs.

It is important to note that although the non-linear filter 30 ismodeled as a concatenation of the non-linear filter model 80 followed bythe linear filter model 82, the non-linear filter 30 is physically asingle device. As such, there is no physical reference point obtainablefrom the non-linear filter 30 that is equivalent to the reference pointat the output of the non-linear filter model 80. The model 78 providesthe needed reference point for adaptive predistortion to compensate forthe non-linear characteristic and not the linear characteristic of thenon-linear filter 30.

FIG. 16 illustrates one embodiment of the adaptor 72 that utilizes themodel 78 of FIG. 15 to adaptively configure the digital predistorter 64to compensate for the non-linear characteristic of the non-linear filter30 according to one embodiment of the present disclosure. Note that theadaptor 72 may be implemented as any suitable type of circuitry such as,for example, one or more Application Specific Integrated Circuits(ASICs) or one or more microprocessors. As illustrated, the adaptor 72includes a first loop, which is referred to herein as a non-linearfilter model identification loop, and a second loop, which is referredto herein as a predistorter model identification loop. The non-linearfilter model identification loop includes the model 78, which asdiscussed above is a concatenation of the non-linear filter model 80followed by the linear filter model 82, and a subtraction function 84.In general, the non-linear filter model identification loop operates toprovide a reference signal at reference point 86. The reference signalat the reference point 86 is referred to herein as a reference signalfor the non-linear characteristic of the non-linear filter 30. Again,the reference signal for the non-linear characteristic of the non-linearfilter 30 is not directly obtainable from the non-linear filter 30 sincethe non-linear filter 30 is a single physical device.

The predistorter model identification loop includes the non-linearfilter model 80, an inverse model 88, and a subtraction function 90. Theinverse model 88 is an inverse model of the non-linear filter model 80.In operation, the predistorter model identification loop obtains theparameters, which in this embodiment are coefficients (C_(PD)), forconfiguring the digital predistorter 64. Specifically, in thisembodiment, since the inverse model 88 is an inverse model of thenon-linear filter model 80 and the non-linear filter model 80 is a modelof the non-linear characteristic of the non-linear filter 30, thecoefficients (C_(PD)) provided to the digital predistorter 64 are thesame coefficients determined for the inverse model 88 via thepredistorter model identification loop.

In operation, the adaptor 72 first trains the non-linear filter model 80using the non-linear filter model identification loop. During thistraining, parameters, which in this embodiment are coefficients, for thenon-linear filter model 80 are determined. Once the non-linear filtermodel 80 is trained, the predistorter model identification loop trainsthe inverse model 88. More specifically, an output signal from thelinear part 52 of the transmitter 28 is provided as an input signal tothe adaptor 72. Once the non-linear filter model 80 is trained, theadaptor 72 provides the input signal of the adaptor 72 to the non-linearfilter model 80, and the non-linear filter model 80 outputs, at thereference point 86, the reference signal for the non-linearcharacteristic of the non-linear filter 30. The adaptor 72 then providesthe reference signal for the non-linear characteristic of the non-linearfilter 30 to the inverse model 88, which then provides a correspondingoutput signal. The subtraction function 90 compares the output of theinverse model 88 and the input signal to the adaptor 72 to provide anerror signal. The error signal represents a difference between theoutput of the inverse model 88 and the input signal of the adaptor 72.The adaptor 72 updates the coefficients for the inverse model 88 basedon the error signal until the error signal is minimized (e.g., until theerror signal is zero or approximately zero). At that point, the inversemodel 88 is trained, and the adaptor 72 provides the coefficients forthe inverse model 88 to the digital predistorter 64 as the coefficients(C_(PD)) for the digital predistorter 64. This process continues suchthat the adaptor 72 continues to update the coefficients for thenon-linear filter model 80, the inverse model 88, and the digitalpredistorter 64 in response to variations in the non-linearcharacteristic of the non-linear filter 30.

Before proceeding, as discussed above with respect to the model 78,while the adaptor 72 of FIG. 16 is shown as being used to adaptivelyconfigure the digital predistorter 64 to compensate for the non-linearcharacteristic of the non-linear filter 30 in the transmitter 28, theadaptor 72 is not limited thereto. The adaptor 72 of FIG. 16 may be usedto adaptively configure a predistorter to compensate for a non-linearcharacteristic of any type of non-linear system or non-linear devicethat has both an undesired non-linear characteristic and a desiredlinear characteristic.

FIG. 17 through 21 describe systems and methods for training thenon-linear filter model 80. Note, however, that the systems and methodsof FIGS. 17 through 21 are exemplary. Other techniques may be used totrain the non-linear filter model 80. However, FIGS. 17 through 21describe one scheme that enables conventional adaptive filteringtechniques to be used to train the non-linear filter model 80.

More specifically, FIG. 17 is a more detailed illustration of thenon-linear filter model 80 according to one embodiment of the presentdisclosure. As shown, the non-linear filter model 80 includes a number(P_(A)) of memory basis functions 92 and a weight and sum function 94.The number P_(A) is equal to the number of coefficients for thenon-linear filter model 80. The memory basis functions 92 receive theinput signal of the non-linear filter model 80, which is denotedx_(A,IN)(n), and output corresponding memory basis function outputsignals x_(A,BF) _(_) _(M) _(_) ₁(n) through x_(A,BF) _(_) _(M) _(_)_(P) _(A) (n). The weight and sum function 94 applies coefficients(C_(A)) for the non-linear filter model 80 as weightings to thecorresponding memory basis function output signals x_(A,BF) _(_) _(M)_(_) ₁(n) through x_(A,BF) _(_) _(M) _(_) _(P) _(A) (n) and then sumsthe weighted basis function output signals to provide the output signalof the non-linear filter model 80, which is denoted as x_(A, OUT)(n).

FIG. 18 is a more detailed illustration of the memory basis functions 92of FIG. 17 according to one embodiment of the present disclosure. Asillustrated, the memory basis functions 92 include a number (K_(A)) ofmemory-less basis functions 96 and a number (K_(A)) of memory structures98-1 through 98-K_(A). Each of the memory structures 98-1 through98-K_(A) has a number (Q_(A)) of taps, where K_(A)×Q_(A)=P_(A). Thememory-less basis functions 96 receive the input signal of thenon-linear filter model 80, which is denoted x_(A, IN)(n), and outputcorresponding memory-less basis function output signals x_(A,BF) _(_)_(ML) _(_) ₁(n) through x_(A,BF) _(_) _(ML) _(_) _(K) _(A) (n). Thememory structures 98-1 through 98-K_(A) receive the memory-less basisfunction output signals x_(A,BF) _(_) _(ML) _(_) ₁(n) through x_(A,BF)_(_) _(ML) _(_) _(P) _(A) (n) and output the memory basis functionoutput signals x_(A,BF M 1)(n) through x_(A,BF M (K) _(A) _(Q) _(A)₎(n).

FIG. 19 illustrates the memory-less basis functions 96 of FIG. 18 inmore detail according to one embodiment of the present disclosure. Asillustrated, the memory-less basis functions 96 includes a number(K_(A)) of memory-less basis functions 100-1 through 100-K_(A).

When looking at the model 78, the weight and sum function 94 where thecoefficients (C_(A)) are applied is at the middle of the model 78. Thisis not desirable for direct application of adaptive filtering schemes tosolve for, or otherwise determine, the coefficients (C_(A)). Rather, itis desirable for the application of the coefficients (C_(A)) to be atthe final stage of the model 78. FIG. 20 illustrates an integrated model102 that is equivalent to the model 78 but where stages have beenrearranged such that the application of the coefficients (C_(A)) is at afinal stage of the integrated model 102. More specifically, in the model78, the weight and sum function 94 and the linear filter model 82 areboth linear. As such, the sequence of the weight and sum function 94 andthe linear filter 82 can be reversed as is done in the integrated model102. In the integrated model 102, the memory basis function outputsignals x_(A,BF) _(_) _(M) _(_) ₁(n) through x_(A,BF) _(_) _(M) _(_)_(P) _(A) (n) are passed through corresponding linear filter models104-1 through 104-P_(A) to provide corresponding basis function outputsignals x_(A,BF) _(_) _(IM) _(_) ₁(n) through X_(A,BF)__(IM) _(_) _(P)_(A)(n). The linear filter models 104-1 through 104-P_(A) are equivalentto the linear filter model 82, which has known coefficients (C_(B)).Thus, the memory basis functions 92 and the linear filter models 104-1through 104-P_(A) become basis functions for the integrated model 102.The weight and sum function 94 then applies the coefficients (C_(A)) asweightings to the corresponding basis function output signals x_(A,BF)_(_) _(IM) _(_) ₁(n) through X_(A,BF) _(_) _(IM) _(_) _(P) _(A) (n) andthen sums the weighted basis function output signals to provide theoutput signal x_(OUT)(n) of the integrated model 102, which isequivalent to the output signal x_(OUT)(n) of the model 78.

Using the integrated model 102, the coefficients (C_(A)) for thenon-linear filter model 80 can be determined using adaptive filtering.Specifically, let a P_(A)×1 vector X_(A,BF) _(_) _(IM)(n) be defined as:X _(A,BF) _(_) _(IM)(n)=[x _(A,BF) _(_) _(IM) _(_) ₁(n), x _(A,BF) _(_)_(IM) _(_) ₂(n), . . . , x _(A,BF) _(_) _(IM) _(_) _(P) _(A)(n)]^(T),where “T” denotes transpose. Over n=n₁, n₂, . . . , n_(N) where n_(N) isthe number of samples used for one adaptation iteration, the memorybasis function output signals x_(A,BF) _(_) _(IM) _(_) ₁(n) throughx_(A,BF) _(_) _(IM) _(_) _(P) _(A) (n) are organized in a N×P_(A) matrixX_(A) as:X _(A) =[X _(A,BF) _(_) _(IM)(n ₁), X _(A,BF) _(_) _(IM)(n ₂), . . . , X_(A,BF) _(_) _(IM)(n _(N))]^(T).A known adaptive filtering algorithm can then be used to solve thefollowing equation for the coefficients (C_(A)) for the non-linearfilter model 80:X _(A) ·C _(A) =X′ _(OUT),where C_(A) is a vector of the coefficients for the non-linear filtermodel 80 defined as:C _(A) =[c _(A) _(_) ₁ , c _(A) _(_) ₂ , . . . , c _(A) _(_) _(P) _(A)]^(T),where c_(A) _(_) ₁, c_(A) _(_) ₂, . . . , C_(A) _(_) _(P) _(A) are thecoefficients for the non-linear filter model 80. X′_(OUT) is defined as:X′ _(OUT) =[x′ _(OUT)(n ₁), x′ _(OUT)(n ₂), . . . , x′ _(OUT)(n_(N))]^(T),where X′_(OUT) is the output of the actual non-linear subsystem, whichin this case is the non-linear filter 30.

FIG. 21 illustrates an embodiment of the adaptor 72 that utilizes theintegrated model 102 of FIG. 20 to train the non-linear filter model 80to adaptively configure the digital predistorter 64 to compensate forthe non-linear characteristic of the non-linear filter 30 according toone embodiment of the present disclosure. This embodiment of the adaptor72 is similar to that of FIG. 16, but where the integrated model 102 isutilized for training the non-linear filter model 80. As illustrated,the adaptor 72 includes a first loop, which is referred to herein as anon-linear filter model identification loop, and a second loop, which isreferred to herein as a predistorter model identification loop. Thenon-linear filter model identification loop includes the integratedmodel 102 and a subtraction function 106 and is utilized by the adaptor72 to train the non-linear filter model 80. More specifically, theoutput of the linear part 52 of the transmitter 28 (or the input of thenon-linear filter 30), is received as the input signal of the adaptor72. The adaptor 72 passes the input signal through the integrated model102 to provide the output signal of the integrated model 102. Thesubtraction function 106 compares the output signal of the integratedmodel 102 and a feedback signal that represents the output signal of thenon-linear filter 30 to provide an error signal that represents adifference between the output signal of the integrated model 102 and thefeedback signal. Based on the error signal, the adaptor 72 trains thecoefficients (C_(A)) for the integrated model 102 until the error signalhas been minimized (e.g., reduced to zero or approximately zero). Thisprocess continues such that the coefficients (C_(A)) are updated inresponse to variations in the non-linear characteristic of thenon-linear filter 30.

The predistorter model identification loop includes the non-linearfilter model 80, the inverse model 88, and the subtraction function 90,as described above with respect to FIG. 16. Again, the inverse model 88is an inverse model of the non-linear filter model 80. In operation,once initial training of the inverse model 102 is complete, thecoefficients (C_(A)) determined for the non-linear filter model 80 usingthe integrated model 102 are utilized in the predistorter modelidentification loop to train the inverse model 88. More specifically,the adaptor 72 passes the input signal of the adaptor 72 through thenon-linear filter model 80 (which is configured with the coefficients(C_(A)) determined using the integrated model 102) to provide thereference signal for the non-linear characteristic of the non-linearfilter 30 at the reference point 86. The adaptor 72 then provides thereference signal for the non-linear characteristic of the non-linearfilter 30 to the inverse model 88, which then provides a correspondingoutput signal. The subtraction function 90 compares the output of theinverse model 88 and the input signal to the adaptor 72 to provide anerror signal. The error signal represents a difference between theoutput of the inverse model 88 and the input signal of the adaptor 72.The adaptor 72 updates the coefficients for the inverse model based onthe error signal until the error signal is minimized (e.g., until theerror signal is zero or approximately zero). At that point, the inversemodel 88 is trained, and the adaptor 72 provides the coefficients forthe inverse model 88 to the digital predistorter 64 as the coefficients(C_(PD)) for the digital predistorter 64. This process continues suchthat the adaptor 72 continues to update the coefficients for thenon-linear filter model 80, the inverse model 88, and the digitalpredistorter 64 in response to variations in the non-linearcharacteristic of the non-linear filter 30.

Before proceeding, again, while the adaptor 72 of FIG. 21 is shown asbeing used to adaptively configure the digital predistorter 64 tocompensate for the non-linear characteristic of the non-linear filter 30in the transmitter 28, the adaptor 72 is not limited thereto. Theadaptor 72 of FIG. 21 may be used to adaptively configure a predistorterto compensate for a non-linear characteristic of any type of non-linearsystem or non-linear device that has both an undesired non-linearcharacteristic and a desired linear characteristic.

FIG. 22 illustrates a system 108 that utilizes the integrated model 102to train a non-linear characteristic of a non-linear subsystem 110according to one embodiment of the present disclosure. The non-linearsubsystem 110 is generally any type of non-linear subsystem thatincludes an undesired non-linear characteristic and a desired linearcharacteristic. Using the integrated model 102, an adaptive filteringtechnique is used in order to train a non-linear model for thenon-linear characteristic of the non-linear subsystem 110 in the mannerdescribed above. Specifically, an input signal, x_(IN)(n), is providedto the non-linear subsystem 110 and the integrated model 102. Asubtraction function 112 compares an output signal, x′_(OUT)(n), of thenon-linear subsystem 110 and an output signal, x_(OUT)(n), of theintegrated model 102 to provide an error signal to the integrated model102 that represents a difference between the two output signalsx_(OUT)(n) and x′_(OUT)(n). Based on the error signal, coefficients forthe integrated model 102, which are also the coefficients for thenon-linear model of the non-linear characteristic of the non-linearsubsystem 110, are updated to minimize the error signal (e.g., updatedto make the error signal zero or approximately zero). The coefficientsdetermined for the non-linear model of the non-linear characteristic ofthe non-linear subsystem 110 may then be used to, for example,predistort the input signal to compensate for the non-linearcharacteristic of the non-linear subsystem 110 in the manner describedabove.

FIG. 23 illustrates another embodiment transmitter 28 including theadaptor 72 that provides bandwidth reduction for the adaptor 72according to one embodiment of the present disclosure. Specifically,this embodiment reduces a bandwidth that the adaptor 72 processes ascompared to a bandwidth of the output signal of the non-linear filter30, which may be at or above the limit of the processing speed ofcurrent state-of-the-art ASICs or microprocessors without employingtechniques specifically for handling higher than clock rate signalprocessing. Reducing the bandwidth being processed by the adaptor 72limits the complexity and thus the cost of implementing the adaptor 72.Reducing the bandwidth also enables linearization for non-linear systemsof wider bandwidths or, in other words, increases a maximum bandwidthfor which linearization can be performed beyond a maximum bandwidth thatcan be handled by the hardware (e.g., ASIC or microprocessor) in whichthe adaptor 72 is implemented. This embodiment of the adaptor 72 issimilar to that of FIG. 16.

For this embodiment, the non-linear filter model 80 is, or can beapproximated as, a memory-less non-linear function. This means that theoutput of the non-linear filter model 80 depends only on the currentinput (or approximately so), and does not give significant contributionto the current output of the non-linear filter model 80. Any dependencyof the output of the non-linear filter model 80 on previous inputs canbe ignored. Because the non-linear filter model 80 is or can beapproximately a memory-less non-linear function, the non-linearcharacteristic of the non-linear filter 30 is frequency independent orcan be approximately assumed to be frequency independent. This can beassumed true as long as the frequency dependency of the non-linearcharacteristic can be modeled by a concatenation of a frequencyindependent non-linear filter model 80 followed by the linear filtermodel 82, which can be frequency dependent.

In order to reduce the bandwidth processed by the adaptor 72, thetransmitter 28 includes a narrowband filter 114 that receives a feedbacksignal that is representative of the output signal of the non-linearfilter 30 and outputs a filtered feedback signal having a significantlyreduced bandwidth. Preferably, the bandwidth of the narrowband filter114 is arbitrarily small. However, in implementation, the bandwidth ofthe narrowband filter 114 is substantially smaller than the bandwidth ofthe output signal of the non-linear filter 30, but the actual bandwidthof the narrowband filter 114 may be a tradeoff between performance andcost/complexity.

As illustrated, the adaptor 72 includes a first loop, which is referredto herein as a non-linear filter model identification loop, and a secondloop, which is referred to herein as a predistorter model identificationloop. The non-linear filter model identification loop includes a model116 of a subsystem formed by the non-linear filter 30 and the narrowbandfilter 114 and the subtraction function 84. The model 116 includes themodel 78 of the non-linear filter 30, which includes the non-linearfilter model 80 and the linear filter model 82, and a narrowband filtermodel 118. The narrowband filter model 118 is a model of the narrowbandfilter 114, which is known. Notably, the narrowband filter 114 may beimplemented in the analog or digital domain, and, likewise, thenarrowband filter model 118 is implemented in the digital domain. Thenarrowband filter model 118 may be known from design or frommeasurements on a per device basis. Notably, while shown separately, thelinear filter model 82 and the narrowband filter model 118 are bothlinear and, as such, can be combined into or treated as a single linearmodel. From this point, the adaptor 72 operates in the same manner asdescribed above with respect to FIG. 16. Further, the integrated model102 (FIG. 21) may be used to train the non-linear filter model 80 in themanner described above.

FIGS. 24A through 24D are frequency domain illustrations of exemplarysignals at reference points A through C in FIG. 23. FIG. 24A illustratesthe input signal to the non-linear filter 30 at reference point A inFIG. 23. As illustrated, the input signal has a wide bandwidth. FIG. 24Billustrates the output signal at the output of the non-linear filter 30at reference point B in FIG. 23. As illustrated, the output signalincludes undesired distortions, including distortions in the passband ofthe non-linear filter 30. FIG. 24C illustrates a frequency response ofthe narrowband filter 114 of FIG. 23. As illustrated, the bandwidth(BW₁) of the narrowband filter 114 is substantially smaller than thebandwidth of the output signal of the non-linear filter 30. FIG. 24Dillustrates the filtered feedback signal (i.e., filtered output signalof the non-linear filter 30) at reference point C of FIG. 23. Asillustrated, the bandwidth of the filtered feedback signal is equal tothe bandwidth (BW₁) of the narrowband filter 114.

Again, while the adaptor 72 of FIG. 23 is shown as being used toadaptively configure the digital predistorter 64 to compensate for thenon-linear characteristic of the non-linear filter 30 in the transmitter28, the adaptor 72 is not limited thereto. As shown in FIG. 25, theadaptor 72 in combination with the digital predistorter 64 and thenarrowband filter 114 can be used to provide adaptive predistortion tocompensate for a non-linear characteristic of any type of non-linearsubsystem 122 (e.g., a non-linear power amplifier).

In the embodiments described herein, various parts can be implemented ineither the analog domain or the digital domain and in either baseband orradio frequency. The concepts disclosed herein do not put restrictionson the detailed implementation, which could be determined jointlyconsidering other aspects of the system.

The following acronyms are used throughout this disclosure.

-   -   4G 4^(th) Generation    -   ADC Analog-to-Digital Converter    -   ASIC Application Specific Integrated Circuit    -   BAW Bulk Acoustic Wave    -   DAC Digital-to-Analog Converter    -   DPD Digital Predistorter    -   FBAR Film Bulk Acoustic Resonator    -   IMD Intermodulation Distortion    -   LTE Long Term Evolution    -   PA Power Amplifier    -   RF Radio Frequency    -   SAW Surface Acoustic Wave    -   W Watt

Those skilled in the art will recognize improvements and modificationsto the preferred embodiments of the present disclosure. All suchimprovements and modifications are considered within the scope of theconcepts disclosed herein and the claims that follow.

What is claimed is:
 1. A system comprising: a non-linear subsystemconfigured to receive an input signal and provide an output signal; apredistorter configured to operate on an input signal of thepredistorter to effect predistortion of the input signal of thenon-linear subsystem to compensate for a non-linear characteristic ofthe non-linear subsystem; a narrowband filter configured to receive afeedback signal representative of the output signal of the non-linearsubsystem and output a filtered feedback signal having a bandwidth thatis less than a bandwidth of the input signal of the predistorter; and anadaptor configured to adaptively configure the predistorter based on thefiltered feedback signal.
 2. The system of claim 1 wherein thenon-linear characteristic of the non-linear subsystem is memory-less. 3.The system of claim 1 wherein the adaptor is configured to adaptivelyconfigure the predistorter based on the filtered feedback signal, aninput signal of the adaptor that is representative of the input signalof the non-linear subsystem, and a model of the non-linear subsystem andthe narrowband filter.
 4. The system of claim 3 wherein the model of thenon-linear subsystem and the narrowband filter is a concatenation of anon-linear model of the non-linear characteristic of the non-linearsubsystem followed by a linear model of the narrowband filter.
 5. Thesystem of claim 3 wherein the model of the non-linear subsystem and thenarrowband filter is a concatenation of a non-linear model of thenon-linear characteristic of the non-linear subsystem followed by atleast one linear model that models a linear characteristic of thenon-linear subsystem and the narrowband filter.
 6. The system of claim 5wherein in order to adaptively configure the predistorter based on thefiltered feedback signal, the input signal of the adaptor, and the modelof the non-linear subsystem and the narrowband filter, the adaptor isfurther configured to: train the non-linear model based on the inputsignal of the adaptor and the filtered feedback signal; and configurethe predistorter based on the non-linear model such that thepredistorter effects predistortion of the input signal of the non-linearsubsystem to compensate for the non-linear characteristic but not thelinear characteristic of the non-linear subsystem.
 7. The system ofclaim 6 wherein in order to configure the predistorter based on thenon-linear model, the adaptor is further configured to: provide theinput signal of the adaptor to the non-linear model such that thenon-linear model outputs a reference signal for the non-linearcharacteristic of the non-linear subsystem; train an inverse model ofthe non-linear model based on the input signal of the adaptor and thereference signal for the non-linear characteristic of the non-linearsubsystem; and provide one or more parameters that define the inversemodel to the predistorter to thereby configure the predistorter.
 8. Thesystem of claim 7 wherein the one or more parameters are a plurality ofcoefficients.
 9. The system of claim 7 wherein in order to train thenon-linear model, the adaptor is further configured to: provide theinput signal of the adaptor to an integrated model such that theintegrated model provides an output signal, wherein the integrated modelis equivalent to the model of the non-linear subsystem and thenarrowband filter but applies coefficients that define the non-linearmodel at a final stage of the integrated model; and configure thenon-linear model of the non-linear subsystem based on the output signalof the integrated model and the filtered feedback signal that representsthe output signal of the non-linear subsystem using an adaptivefiltering scheme.
 10. The system of claim 9 wherein the integrated modelcomprises: a plurality of memory basis functions of the non-linear modelthat provide a corresponding plurality of memory basis function outputsignals based on the input signal of the adaptor; a plurality of linearmodels each corresponding to the at least one linear model that modelsthe linear characteristic of the non-linear subsystem and the narrowbandfilter, wherein the plurality of linear models receive the plurality ofmemory basis function output signals from the plurality of memory basisfunctions of the non-linear model and output a corresponding pluralityof memory basis function output signals for the integrated model; and aweight and sum function that weights and sums the plurality of memorybasis function output signals for the integrated model based on aplurality of coefficients for the non-linear model to provide the outputsignal of the integrated model.
 11. A transmitter comprising: a poweramplifier configured to amplify a radio frequency input signal toprovide an amplified radio frequency signal; a non-linear filterconfigured to receive the amplified radio frequency signal as an inputsignal of the non-linear filter and filter the amplified radio frequencysignal to provide an output signal of the non-linear filter, thenon-linear filter having a linear characteristic and a non-linearcharacteristic; a predistorter configured to operate on an input signalof the predistorter to effect predistortion of the input signal of thenon-linear filter to compensate for the non-linear characteristic of thenon-linear filter; a narrowband filter configured to receive a feedbacksignal representative of the output signal of the non-linear filter andoutput a filtered feedback signal having a bandwidth that is less than abandwidth of the input signal of the predistorter; and an adaptorconfigured to adaptively configure the predistorter based on thefiltered feedback signal.
 12. The transmitter of claim 11 wherein thenon-linear characteristic of the non-linear filter is memory-less. 13.The transmitter of claim 11 wherein the adaptor is configured toadaptively configure the predistorter based on the filtered feedbacksignal, an input signal of the adaptor that is representative of theinput signal of the non-linear filter, and a model of the non-linearfilter and the narrowband filter.
 14. The transmitter of claim 13wherein the model of the non-linear filter and the narrowband filter isa concatenation of a non-linear filter model of the non-linearcharacteristic of the non-linear filter followed by a linear filtermodel of the narrowband filter.
 15. The transmitter of claim 13 whereinthe model of the non-linear filter and the narrowband filter is aconcatenation of a non-linear filter model of the non-linearcharacteristic of the non-linear filter followed by at least one linearfilter model that models a linear characteristic of the non-linearfilter and the narrowband filter.
 16. The transmitter of claim 15wherein in order to adaptively configure the predistorter based on thefiltered feedback signal, the input signal of the adaptor, and the modelof the non-linear filter and the narrowband filter, the adaptor isfurther configured to: train the non-linear filter model based on theinput signal of the adaptor and the filtered feedback signal; andconfigure the predistorter based on the non-linear filter model suchthat the predistorter effects predistortion of the input signal of thenon-linear filter to compensate for the non-linear characteristic butnot the linear characteristic of the non-linear filter.
 17. Thetransmitter of claim 16 wherein in order to configure the predistorterbased on the non-linear filter model, the adaptor is further configuredto: provide the input signal of the adaptor to the non-linear filtermodel such that the non-linear filter model outputs a reference signalfor the non-linear characteristic of the non-linear filter; train aninverse model of the non-linear filter model based on the input signalof the adaptor and the reference signal for the non-linearcharacteristic of the non-linear filter; and provide one or moreparameters that define the inverse model to the predistorter to therebyconfigure the predistorter.
 18. The transmitter of claim 17 wherein theone or more parameters are a plurality of coefficients.
 19. Thetransmitter of claim 17 wherein in order to train the non-linear filtermodel, the adaptor is further configured to: provide the input signal ofthe adaptor to an integrated model such that the integrated modelprovides an output signal, wherein the integrated model is equivalent tothe model of the non-linear filter and the narrowband filter but appliescoefficients that define the non-linear filter model at a final stage ofthe integrated model; and configure the non-linear filter model of thenon-linear filter based on the output signal of the integrated model andthe filtered feedback signal that represents the output signal of thenon-linear subsystem using an adaptive filtering scheme.
 20. Thetransmitter of claim 19 wherein the integrated model comprises: aplurality of memory basis functions of the non-linear filter model thatprovide a corresponding plurality of memory basis function outputsignals based on the input signal of the adaptor; a plurality of linearmodels each corresponding to the at least one linear filter model thatmodels the linear characteristic of the non-linear filter and thenarrowband filter, wherein the plurality of linear models receive theplurality of memory basis function output signals from the plurality ofmemory basis functions of the non-linear filter model and output acorresponding plurality of memory basis function output signals for theintegrated model; and a weight and sum function that weighs and sums theplurality of memory basis function output signals for the integratedmodel based on a plurality of coefficients for the non-linear filtermodel to provide the output signal of the integrated model.